{
  "status": "PASS",
  "assertions": 2866,
  "groups": {
    "pick_and_refinement": 110,
    "pick_dilation_closed": 440,
    "pick_dilation_interior": 440,
    "half_open_height_and_reflection": 28,
    "cone_closed_against_inequalities": 364,
    "cone_interior_against_inequalities": 336,
    "fan_closed_inclusion_exclusion": 84,
    "six_residue_formula": 241,
    "six_residue_reciprocity": 240,
    "lower_dimensional_closed": 125,
    "relative_interior_reciprocity": 120,
    "reeve_fundamental_domain": 16,
    "reeve_closed": 96,
    "reeve_interior": 80,
    "period_collapse": 101,
    "all_half_open_complements": 20,
    "invalid_input_rejected": 9,
    "certificate_round_trip": 1,
    "damaged_certificate_rejected": 4,
    "affine_unimodular_point_bijection": 10,
    "large_parameter_2026": 1
  },
  "capstone": {
    "pick": {
      "vertices": [
        [
          0,
          0
        ],
        [
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        ],
        [
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          3
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      ],
      "area_twice": 12,
      "I": 3,
      "B": 8,
      "triangles": [
        [
          [
            0,
            3
          ],
          [
            0,
            2
          ],
          [
            1,
            2
          ]
        ],
        [
          [
            0,
            2
          ],
          [
            2,
            1
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          [
            1,
            2
          ]
        ],
        [
          [
            2,
            1
          ],
          [
            4,
            0
          ],
          [
            1,
            2
          ]
        ],
        [
          [
            4,
            0
          ],
          [
            0,
            3
          ],
          [
            1,
            2
          ]
        ],
        [
          [
            0,
            2
          ],
          [
            0,
            1
          ],
          [
            1,
            1
          ]
        ],
        [
          [
            0,
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          [
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            0
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          [
            1,
            1
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        ],
        [
          [
            4,
            0
          ],
          [
            2,
            1
          ],
          [
            1,
            1
          ]
        ],
        [
          [
            2,
            1
          ],
          [
            0,
            2
          ],
          [
            1,
            1
          ]
        ],
        [
          [
            0,
            0
          ],
          [
            1,
            0
          ],
          [
            0,
            1
          ]
        ],
        [
          [
            1,
            0
          ],
          [
            2,
            0
          ],
          [
            0,
            1
          ]
        ],
        [
          [
            2,
            0
          ],
          [
            3,
            0
          ],
          [
            0,
            1
          ]
        ],
        [
          [
            3,
            0
          ],
          [
            4,
            0
          ],
          [
            0,
            1
          ]
        ]
      ],
      "triangle_determinants": [
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1,
        1
      ],
      "V": 11,
      "E": 22,
      "T": 12,
      "boundary_edges": 8,
      "edge_multiplicities": {
        "1": 8,
        "2": 14
      }
    },
    "rational_triangle": {
      "vertices": [
        [
          0,
          0
        ],
        [
          "1/2",
          0
        ],
        [
          0,
          "1/3"
        ]
      ],
      "dimension": 2,
      "q": 6,
      "direction": [
        "1/7",
        "4/21",
        1
      ],
      "pieces": [
        {
          "vertices": [
            [
              0,
              0
            ],
            [
              "1/2",
              0
            ],
            [
              0,
              "1/3"
            ]
          ],
          "beta": [
            "1/42",
            "1/21",
            "2/21"
          ],
          "closed_strict": [],
          "closed_numerator": {
            "0": 1,
            "1": 1,
            "2": 2,
            "3": 3,
            "4": 4,
            "5": 5,
            "6": 4,
            "7": 5,
            "8": 4,
            "9": 3,
            "10": 2,
            "11": 1,
            "12": 1
          },
          "interior_numerator": {
            "6": 1,
            "7": 1,
            "8": 2,
            "9": 3,
            "10": 4,
            "11": 5,
            "12": 4,
            "13": 5,
            "14": 4,
            "15": 3,
            "16": 2,
            "17": 1,
            "18": 1
          }
        }
      ],
      "numerator": {
        "0": 1,
        "1": 1,
        "2": 2,
        "3": 3,
        "4": 4,
        "5": 5,
        "6": 4,
        "7": 5,
        "8": 4,
        "9": 3,
        "10": 2,
        "11": 1,
        "12": 1
      },
      "interior_numerator": {
        "6": 1,
        "7": 1,
        "8": 2,
        "9": 3,
        "10": 4,
        "11": 5,
        "12": 4,
        "13": 5,
        "14": 4,
        "15": 3,
        "16": 2,
        "17": 1,
        "18": 1
      }
    },
    "rational_closed_0_to_18": [
      1,
      1,
      2,
      3,
      4,
      5,
      7,
      8,
      10,
      12,
      14,
      16,
      19,
      21,
      24,
      27,
      30,
      33,
      37
    ],
    "rational_interior_1_to_18": [
      0,
      0,
      0,
      0,
      0,
      1,
      1,
      2,
      3,
      4,
      5,
      7,
      8,
      10,
      12,
      14,
      16,
      19
    ],
    "negative_seven": 1,
    "geometric_negative_seven": 8,
    "period_collapse": {
      "vertices": [
        [
          0,
          0
        ],
        [
          2,
          0
        ],
        [
          0,
          "1/2"
        ]
      ],
      "dimension": 2,
      "q": 2,
      "direction": [
        "4/7",
        "2/7",
        1
      ],
      "pieces": [
        {
          "vertices": [
            [
              0,
              0
            ],
            [
              2,
              0
            ],
            [
              0,
              "1/2"
            ]
          ],
          "beta": [
            "1/14",
            "1/7",
            "2/7"
          ],
          "closed_strict": [],
          "closed_numerator": {
            "0": 1,
            "1": 3,
            "2": 3,
            "3": 1
          },
          "interior_numerator": {
            "3": 1,
            "4": 3,
            "5": 3,
            "6": 1
          }
        }
      ],
      "numerator": {
        "0": 1,
        "1": 3,
        "2": 3,
        "3": 1
      },
      "interior_numerator": {
        "3": 1,
        "4": 3,
        "5": 3,
        "6": 1
      }
    },
    "complement_demo": {
      "columns": [
        [
          0,
          2
        ],
        [
          3,
          2
        ]
      ],
      "closed_points": [
        [
          0,
          0
        ],
        [
          0,
          1
        ],
        [
          1,
          1
        ],
        [
          1,
          2
        ],
        [
          2,
          2
        ],
        [
          2,
          3
        ]
      ],
      "open_points": [
        [
          1,
          1
        ],
        [
          1,
          2
        ],
        [
          2,
          2
        ],
        [
          2,
          3
        ],
        [
          3,
          3
        ],
        [
          3,
          4
        ]
      ]
    },
    "large_parameter_2026": {
      "closed": 343070,
      "interior": 341044,
      "direct_closed": 343070,
      "direct_interior": 341044
    }
  },
  "limits": [
    "Finite exact tests do not replace proofs.",
    "Only positive dilations have interior-count semantics.",
    "Negative evaluation follows the quasipolynomial, not geometric reflection.",
    "Enumeration cost may be large in the bit size, denominator and dimension."
  ]
}